Sequential and Mapreduce-based Algorithms for Constructing an In-place Multidimensional Quad-tree Index for Answering Fixed-radius Nearest Neighbor Queries

Answering fixed-radius nearest neighbor queries constitutes an important problem in many areas, ranging from geographic systems to similarity searching in object databases (e.g. image and video databases). The usual approach in order to efficiently answer such queries is to construct an index. In this paper we present algorithms for constructing a multidimensional quad-tree index. We start with well-known sequential algorithms and then adapt them to the MapReduce computation model, in order to be able to handle large amounts of data. In all the algorithms the objects are indexed in association with quad-tree cells (or nodes) which they intersect (plus possibly a few other nearby cells). When processing a query, multiple quad-tree cells may be searched in order to find the answer. 2010 Mathematics Subject Classification:68P05, 68P10, 68P15, 68P20, 68U35, 68W10, 68W15.